On the Uq[sl(2)]{\cal{U}}_{q}[sl(2)] Temperley-Lieb reflection matrices

This work concerns the boundary integrability of the spin-s ${\cal{U}}_{q}[sl(2)]$ Temperley-Lieb model. A systematic computation method is used to constructed the solutions of the boundary Yang-Baxter equations. For $s$ half-integer, a general $2s(s+1)+3/2$ free parameter solution is presented. It turns that for $s$ integer, the general solution has $2s(s+1)+1$ free parameters. Moreover, some particular solutions are discussed.Comment: LaTex 17 page

Exact Lyapunov Exponent for Infinite Products of Random Matrices

In this work, we give a rigorous explicit formula for the Lyapunov exponent for some binary infinite products of random $2\times 2$ real matrices. All these products are constructed using only two types of matrices, $A$ and $B$, which are chosen according to a stochastic process. The matrix $A$ is singular, namely its determinant is zero. This formula is derived by using a particular decomposition for the matrix $B$, which allows us to write the Lyapunov exponent as a sum of convergent series. Finally, we show with an example that the Lyapunov exponent is a discontinuous function of the given parameter.Comment: 1 pages, CPT-93/P.2974,late

Beyond Mean-Field Low-Lying Excitations of Dipolar Bose Gases

We theoretically investigate various beyond mean-field effects on Bose gases at zero temperature featuring the anisotropic and long-range dipole-dipole interaction in addition to the isotropic and short-range contact interaction. Within the realm of the Bogoliubov-de Gennes theory, we consider static properties and low-lying excitations of both homogeneous and harmonically trapped dipolar bosonic gases. For the homogeneous system, the condensate depletion, the ground-state energy, the equation of state, and the speed of sound are discussed in detail. Making use of the local density approximation, we extend these results in order to study the properties of a dipolar Bose gas in a harmonic trap and in the regime of large particle numbers. After deriving the equations of motion for the general case of a triaxial trap, we analyze the influence of quantum fluctuations on important properties of the gas, such as the equilibrium configuration and the low-lying excitations in the case of a cylinder-symmetric trap. In addition to the monopole and quadrupole oscillation modes, we also discuss the radial quadrupole mode. We find that the latter acquires a quantum correction exclusively due to the dipole-dipole interaction. As a result, we identify the radial quadrupole as a reasonably accessible source for the signature of dipolar many-body effects and stress the enhancing character that dipolar interactions have for quantum fluctuations in the other oscillation modes.Comment: Version published in PR

Accelerating Cold Dark Matter Cosmology (ΩΛ≡0\Omega_{\Lambda}\equiv 0)

A new kind of accelerating flat model with no dark energy that is fully dominated by cold dark matter (CDM) is investigated. The number of CDM particles is not conserved and the present accelerating stage is a consequence of the negative pressure describing the irreversible process of gravitational particle creation. A related work involving accelerating CDM cosmology has been discussed before the SNe observations [Lima, Abramo & Germano, Phys. Rev. D53, 4287 (1996)]. However, in order to have a transition from a decelerating to an accelerating regime at low redshifts, the matter creation rate proposed here includes a constant term of the order of the Hubble parameter. In this case, $H_0$ does not need to be small in order to solve the age problem and the transition happens even if the matter creation is negligible during the radiation and part of the matter dominated phase. Therefore, instead of the vacuum dominance at redshifts of the order of a few, the present accelerating stage in this sort of Einstein-de Sitter CDM cosmology is a consequence of the gravitational particle creation process. As an extra bonus, in the present scenario does not exist the coincidence problem that plagues models with dominance of dark energy. The model is able to harmonize a CDM picture with the present age of the universe, the latest measurements of the Hubble parameter and the Supernovae observations.Comment: 9 pages, 6 figures, typos corrected, references added, discussion in Appendix B extende

Exact solution of A-D Temperley-Lieb Models

We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups {\cal U}_q(X_n } for X_n = A_1,B_n,C_n$and$D_n$. We employ a generalization of the coordinate Bethe-Ansatz developed previously for the deformed biquadratic spin one chain. As expected, all these models have equivalent spectra, i.e. they differ only in the degeneracy of their eigenvalues. This is true for finite length and open boundary conditions. For periodic boundary conditions the spectra of the lower dimensional representations are containded entirely in the higher dimensional ones. The Bethe states are highest weight states of the quantum group, except for some states with energy zero

Awaking the vacuum in relativistic stars

Void of any inherent structure in classical physics, the vacuum has revealed to be incredibly crowded with all sorts of processes in relativistic quantum physics. Yet, its direct effects are usually so subtle that its structure remains almost as evasive as in classical physics. Here, in contrast, we report on the discovery of a novel effect according to which the vacuum is compelled to play an unexpected central role in an astrophysical context. We show that the formation of relativistic stars may lead the vacuum energy density of a quantum field to an exponential growth. The vacuum-driven evolution which would then follow may lead to unexpected implications for astrophysics, while the observation of stable neutron-star configurations may teach us much on the field content of our Universe.Comment: To appear in Phys. Rev. Let

Cosmological Inhomogeneities with Bose-Einstein Condensate Dark Matter

We consider the growth of cosmological perturbations to the energy density of dark matter during matter domination when dark matter is a scalar field that has undergone Bose-Einstein condensation. We study these inhomogeneities within the framework of both Newtonian gravity, where the calculation and results are more transparent, and General Relativity. The direction we take is to derive analytical expressions, which can be obtained in the small pressure limit. Throughout we compare our results to those of the standard cosmology, where dark matter is assumed pressureless, using our analytical expressions to showcase precise differences. We find, compared to the standard cosmology, that Bose-Einstein condensate dark matter leads to a scale factor, gravitational potential and density contrast that increase at faster rates.Comment: 17 pages, 2 figures; typos corrected, references adde

On the shape of barchan dunes

Barchans are crescent-shaped sand dunes forming in aride regions with unidirectional wind and limited sand supply. We report analytical and numerical results for dune shapes under different environmental conditions as obtained from the so-called `minimal model' of aeolian sand dunes. The profiles of longitudinal vertical slices (i.e. along the wind direction) are analyzed as a function of wind speed and sand supply. Shape transitions can be induced by changes of mass, wind speed and sand supply. Within a minimal extension of the model to the transverse direction the scale-invariant profile of transverse vertical cuts can be derived analytically.Comment: to appear in J. Phys.: Condens. Matter 17 (2005